-6x-21=51/3x

Solution for -6x-21=51/3x equation:

-6x-21=51/3x

We move all terms to the left:

-6x-21-(51/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-6x-(+51/3x)-21=0

We get rid of parentheses

-6x-51/3x-21=0

We multiply all the terms by the denominator


-6x*3x-21*3x-51=0

Wy multiply elements

-18x^2-63x-51=0

a = -18; b = -63; c = -51;
Δ = b2-4ac
Δ = -632-4·(-18)·(-51)
Δ = 297
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-3\sqrt{33}}{2*-18}=\frac{63-3\sqrt{33}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+3\sqrt{33}}{2*-18}=\frac{63+3\sqrt{33}}{-36}
$